The overall goal of this project is to develop models of, and computational strategies for analyzing, the dynamics of interacting closed--loop physiological systems. Specifically, the project focusses on the problem of better understanding the dynamic mechanisms that underlie the complex interactions between respiratory control and control of sleep--wake state. We hypothesize that the complex dynamics generated by these interacting systems account for the changes in sleep and respiration observed during sleep--disordered breathing. A computational procedure, employing autoregressive modeling, has been developed to quantitate chemoreflex dynamics from measurements of the ventilatory response to pulses of inspired $CO_{2}$ modulated in the form of a pseudorandom binary sequence. With the aid of accompanying simulations using an existing model of respiratory control, we have been able to circumvent the problem of large estimation error produced by the limited bandwidth of the stimulus signal (i.e., end--tidal P$_{CO2}$). This is achieved by transforming the computed model structure into the frequency domain. This method produces theoretically accurate results for estimated chemoreflex dynamics in the 0.01 to 0.03 Hz range, a span compatible to the periodicities observed in sleep--disordered breathing. The ventilatory response to arousal, net of any confounding effects from the chemoreflexes, has also been studied. This was achieved by studying the respiratory responses of subjects briefly aroused from sleep by short loud tones. We have found these responses to be mediated primarily by the restoration of the neural drive to breathe, rather than by transient changes in upper airway mechanics. These empirical results will be used to refine our existing model of sleep--disordered breathing.